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arXiv · 1801.00486

On the third moment of $L\big(\frac{1}{2}, \chi_{d}\big)$ I: the rational function field case

Adrian Diaconu
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Abstract

In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions $$\sum_{\substack{d - \mathrm{monic \, \& \, sq. \, free} \mathrm{deg}\, d \, = \, D}} L\big(\tfrac{1}{2}, \chi_{d}\big)^{3}$$ over rational function fields on the order of $q^{\scriptscriptstyle \frac{3}{4} D}.$ This term is in perfect analogy with the $x^{\scriptscriptstyle \frac{3}{4}}$-term indicated in our joint work arXiv:math/0110092v1 for the corresponding asymptotic formula over the rationals.

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Adrian Diaconu. 2018-01-01. On the third moment of $L\big(\frac{1}{2}, \chi_{d}\big)$ I: the rational function field case. https://arxiv.org/abs/1801.00486

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